# How to search for duplicate of this classic complex analysis question?

## Aim

A quick search for .

## Question

If $|f(z) |\leq 1 + |z|$, show that $f(z) = az + b$ is a recently-posted question. I tried to search for its duplicates on Approach0 but I didn't manage to get something like Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$..

How can I search for dupes of this question on the main site and/or Approach0?

• Interestingly, if I take the search you linked and omit all occurrences of \left... and \right.... then it appears near the top. I am not sure whether this should make much difference - I have asked about this in the searching chatroom. Nov 26, 2020 at 10:56
• @MartinSleziak Thanks for comment. The left and right are automatically generated by the search page's input text field/area. Nov 26, 2020 at 11:10
• I see. I only use the "raw query" to input formulas in Approach0. (Either by directly entering/editing LaTeX, or by copy-paste - and I have a bookmarklet to make copy-paste faster.) So I have no experience with entering a math formula with that editor which is used there. Nov 26, 2020 at 11:15
• I think finding the right search terms is as much an art as a science. After trying a few other things, I found that searching on math.stackexchange for "linear function" [complex-analysis] got me the duplicate. (The [complex-analysis] restricts the search to questions tagged complex-analysis.) Nov 26, 2020 at 11:23
• @GNUSupporter8964民主女神地下教會 A0 author here. As MartinSleziak pointed out, you need to strip those \left and \right around "vertical bar" to find that post. I did not find a good way to parse vertical bars used in representing absolute values if they do not have \left \right to help me parse, what I do is simply treat a single bar as a leaf token. That is why you see the difference as in original post it does not have \left \right surrounded, and you need to use the same representation in your query to find that post. Nov 27, 2020 at 3:23
• @WeiZhong Thanks for your answer. Lemme write a "solution" when I've time now so that this question is treated as resolved. Nov 27, 2020 at 7:24
• I've collected all the duplicates that I could find in an answer to "The duplicate thread". Feb 4 at 21:12

So for example: \leq "integral formula" gives around 350 results and fine-tuning to "f(z)" \leq "integral formula" yields 223. We can also try variants like \le in place of \leq which interestingly gives fewer hits.
Probably this question was asked partly due to the fact that the post did not appear in the search results in Approach0. The reason is that this search engine differentiates between \left|...\right| and |....|. (On the other hand, \left(...\right) or \left{...right} are treated the same as (...) or {...}. In this case, the shape of the bracket already indicates whether it is left or right bracket.
In particular, this is the search query linked in the question - and here is the same query where \left|...\right| was replaced by |....|. The question Showing that $$f$$ is linear function if $$\forall z \in \mathbb{C}$$, $$|f(z)| \leq 1 + |z|$$ is among the top results only for the latter query.